Jose Mourinho is eager to go on a huge spending spree in the summer, and he is eyeing a world-class replacement for the injured Zlatan Ibrahimovic.
Morata, who has also gleaned interest from Chelsea, has been sounded out as a United target too.
But Sky Italia claim Real have turned down a £52.4million offer from the Red Devils.
It is suggested the bid tabled was just for Morata and didn’t include David De Gea, who is wanted by Los Blancos president Florentino Perez as a replacement for Keylor Navas.
Manchester United line-up next season with Alvaro Morata Tue, June 6, 2017
Click through the gallery for Manchester United's possible line-up next season with Alvaro Morata
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GK: David de Gea
Manchester United have had an offer rejected for Alvaro Morata
Manchester United have £52.4million offer for Alvaro Morata rejected
The report adds Real are demanding £78.6m for his services.
Should United fail to sign Morata, they will turn their attentions to sign Torino striker Andrea Belotti, who has an £87.4m release clause in his contract.
The Red Devils have no shortage of striker targets, with Romelu Lukaku and Paulo Dybala on their hitlist.
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The offer didn't include David De Gea
Everton hitman Lukaku dropped a hint he will stay in the Premier League, although he has yet to publicly reveal his next destination.
He told Sky Sports: “My agent knows what's going to happen.
"I know what I want to do, and whenever something happens, you guys will know."